how to extract RLC equivalent circuit from S-parameter

s parameter transfer to rlc model

Hi there:

Can someone give me any suggestion about
how to extract RCL equivalent circuit from
S parameter?

If I have S parameter of a 4-port network,
how to garantee that there is no negative
elements (C,L,R) in the final extracted circuits?

Thanks.

Div

s parameter to rlc model

First of all , there should be a model of your 4-port box. Otherwise , to obtain RLC components is not possible. Because each model will give possible RLC values.

If you can model your black-box , develop transfer function in the terms of S-parameters and then put the values in it .

For instance , a spiral inductor on the silicon substrate has been modelized a low pass filter form ( you can also do that ) and this circuit has a transfer function in the terms of S-parameters ( or Y-parameters or Z ..etc..) .
Once all the parameters has been defined well , you can extract your others..

GL

several limitations

There are two limitation. If your circuit has gain (|S21|>1), no passive network will be equivalent to it. Passive RLC two port circuits have the 21 parameter equal to the 12 parameter. You cannot make a passive equivalent to an active circuit. If these conditions are met it is possible with a passive network.
You can do a brute force method of converting the S parameters to Y or Z parameters. This can be done by hand or with a utility program such as Veripol which is part of ad lab at https://people.freenet.de/weberconnect_free/adlabp2.htm You can use it something like 20 times before requiring the share ware payment. You type in the S parameters and click the two port ones you want.

Next you find the Z or Y parameters of a passive T or Pi network with lumped impedances in the three legs (not the equivalent network with two generators). Then you find the impedance of each of the three branches and then use ordinary one port synthesis procedures.

This last paragraph sounds complex, but most old passive network theory books used in a first course on networks will have it alredy done. You can follow the examples in the book. For instance, in a T network using the Z parameters, Z11 equals the series branch on the port 1 end plus the shunt branch. Z12=Z21 equals the shunt branch in the center. Z22 equals the shunt branch plus the series branch at the port 2 end.

If you end up with negative real parts, you will have to use a bridge circuit which can have any parameters that have positive real parts.

Div-
ADS has a utility that has some predefined topologies that it will optimize based on sparameters at a single frequency.

Extraction of S-parameters

Hi pal,
I have a unique method that requires the knowledge of interpolation and from the poles derive the required R, L, C equivalent circuit.

From the four set of S-parameters (both real and imaginary), equate them to four set of cauchy interpolation rational function. By moving the denominator over to the know S-parameters and grouping the equations into AX=b, these unknown can be solved by total least square method. Note for the existence of b column matrix, the a0 of the denominator should be set to 1.

After finding the cauchy coefficients for both the numerator and denominator, perform a S to Y transformation and then, factorize both the numerator and denominator into their roots. From the concept of poles and zeros, one can deduce the required optimal equivalent from the concept of Y-parameters.

Hope this will give you some thought.

:wink: :wink: :wink: :wink: :wink:

Re: Extraction of S-parameters

Thank yingyang for the detaiedl explanation.
Is this what people called "macro-modeling"?

Div.

rlc extraction

That is affirmative.

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